Republican presidential candidate Donald Trump wants more than a wall to keep out immigrants living in the country illegally. He also wants to end ‘‘birthright citizenship’’ for their children, he said Sunday. And he would rescind Obama administration executive orders on immigration and toughen deportation, allowing in only ‘‘the good ones.’’

Trump described his expanded vision of how to secure American borders during a wide-ranging interview Sunday on NBC’s ‘‘Meet The Press,’’ saying that he would push to end the constitutionally protected citizenship rights of children of any family living illegally inside the US

‘‘They have to go,’’ Trump said, adding: ‘‘What they’re doing, they’re having a baby. And then all of a sudden, nobody knows...the baby’s here.’’

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Native-born children of immigrants — even those living illegally in the US — have been automatically considered American citizens since the adoption of the 14th amendment of the US Constitution in 1868.

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The odds of repealing the amendment’s citizenship clause would be steep, requiring the votes of two-thirds of both houses of Congress and support from three-fourths of the nation’s state legislatures. Republicans in Congress have repeatedly failed since 2011 to pass bills aimed at ending ‘‘birthright citizenship.’’ Some conservatives believe the provision could be changed without amending the Constitution.

‘‘They’re illegal,’’ Trump said about families that might face deportation. ‘‘You either have a country or not.’’

Trump’s remarks came as his campaign website posted his program for ‘‘immigration reform.’’ Among its details: Making Mexico pay for a permanent border wall. Mandatory deportation of all ‘‘criminal aliens.’’ Tripling the force of immigration officers by eliminating tax credit payments to immigrant families residing illegally in the US.

He said that families with US-born children could return quickly if deemed worthy by the government. ‘‘We’re going to try and bring them back rapidly, the good ones,’’ he said, adding: ‘‘We will expedite it so people can come back in. The good people can come back.’’

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Trump did not elaborate on how he would define ‘‘good people.’’ But echoing earlier controversial remarks that Mexico was sending criminals across the border, Trump said a tough deportation policy was needed because ‘‘there’s definitely evidence’’ of crimes linked to immigrants living in the country illegally.

The a New York businessman said he would waste little time rescinding President Barack Obama’s executive actions aimed at allowing as many as 3.7 million immigrants living illegally in the US to remain in the country because of their US-born relatives. Obama’s November 2014 actions were halted by temporary injunctions ordered by several federal courts in rulings challenging his executive powers to alter immigration policies without Congressional approval. The cases could lead to the US Supreme Court.

‘‘We have to make a whole new set of standards,’’ Trump said. ‘‘And when people come in, they have to come in legally.’’

Trump’s plan was endorsed by Sen. Jeff Sessions, R-Ala., who chairs a Senate subcommittee on immigration.

‘‘This is exactly the plan America needs,’’ Sessions said in a statement. ‘‘Crucially, this plan includes an emphasis on lifting struggling minority communities, including our immigrant communities, out of poverty, by preventing corporations from bringing in new workers from overseas to replace them and drive down wages.’’

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On Sunday, Ohio Gov. John Kasich echoed Trump’s call to finish construction of an incomplete system of barriers on the nation’s southern border with Mexico. There are still gaps in the barriers, which have been under construction since 2005.

Speaking on CBS’ ‘‘Face the Nation,’’ Kasich said he would ‘‘finish the wall’’ but would then work to legalize 12 million immigrants now estimated to live in the US illegally. Kasich said he would ‘‘make sure we don’t have anybody — any of the criminal element here.’’ He would also revive the guest-worker programs that previously brought in temporary workers to aid in farming and other industries hobbled by labor shortages.

Most other GOP candidates also back completing the border wall but differ over how to treat immigrant families already living in the US Former Florida Gov. Jeb Bush recently released his own immigration plan calling for the use of forward bases and drones to guard the border, but also backing an eventual plan to legalize the status of immigrant families. Bush disagrees with Obama’s use of executive actions to unilaterally enforce the policy.

Florida Sen. Marco Rubio worked with senators from both parties to develop a comprehensive plan in 2013 that would have legalized the status of many immigrant families. But Congress balked at the idea as tea party Republicans opposed the deal and Rubio has since backed away from his support.